Question: Umaima is 4 times as old as Gabriela. Eight years ago, Umaima was 6 times as old as Gabriela. How old is Umaima now?
Answer: We can use the given information to write down two equations that describe the ages of Umaima and Gabriela. Let Umaima's current age be $u$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $u = 4g$ Eight years ago, Umaima was $u - 8$ years old, and Gabriela was $g - 8$ years old. The information in the second sentence can be expressed in the following equation: $u - 8 = 6(g - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = u / 4$ . Substituting this into our second equation, we get: $u - 8 = 6($ $(u / 4)$ $- 8)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $u - 8 = \dfrac{3}{2} u - 48$ Solving for $u$ , we get: $\dfrac{1}{2} u = 40$ $u = 2 \cdot 40 = 80$.